{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This is a data simulation that is meant to show several things: <br>\n",
    "<ul>\n",
    "<li>How to simule a bernoulli random event</li>\n",
    "<li>How to build a Logistic Regression using Sci-kit learn</li>\n",
    "<li>Visualize a linear separating hyperplane </li>\n",
    "<li>Use the prior 3 steps to better understand overfitting.</li>\n",
    "</ul>\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>First we import necessary libraries and set up functions that can generate a random bernoulli dataset.<br> \n",
    "We input the parameters of the linear hyperplane and get a dataset with $X=<x_1, x_2>$ and $Y \\in [0,1]$</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "import math\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import linear_model\n",
    "\n",
    "def getP(val):\n",
    "    '''\n",
    "    Get f(x) where f is the logistic function...returns a probability\n",
    "    '''\n",
    "    return (1 + math.exp(-1*val))**-1\n",
    "\n",
    "def getY(val):\n",
    "    '''\n",
    "    Return a binary indicator based on a binomial draw with prob = f(val), f being the logistic function.\n",
    "    '''\n",
    "    return (int(getP(val) > np.random.uniform(0, 1, 1)[0]))\n",
    "\n",
    "def gen_logistic_dataframe(n, alpha, betas):\n",
    "    '''\n",
    "    A function that generates a random logistic dataset.\n",
    "    n is the number of samples\n",
    "    Alpha, betas are the logistic truth, where alpha is the intercept and betas coefficients for vectors.\n",
    "    Uses the shape of betas to determine number of features generated.\n",
    "    '''\n",
    "    X = np.random.random([n, len(betas)])\n",
    "    Y = list(map(getY, X.dot(betas) + alpha))\n",
    "    d = pd.DataFrame(X, columns= ['f'+ str(j) for j in range(X.shape[1])])\n",
    "    d['Y'] = Y\n",
    "    return d\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for this example we'll generate some data. We let the truth actually be random. We do it this way so we can surprise ourselves with what our models actually learn. \n",
    "\n",
    "We'll also plot it. When we look at the plot, try and guess where the separating line should be?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11a8b8390>"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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U9OjQ9xf6j409xt2flvSkpJdV0UDkpdeT1telra3iK8EMRIBhr8o1Wq1tZqfN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\nmP8HNRkT4wHlRPsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "n = 100\n",
    "alpha = np.random.randint(-2,2)\n",
    "beta = np.array([np.random.randn()*2, np.random.randn()*2])\n",
    "#beta = np.array([5, -5])\n",
    "data = gen_logistic_dataframe(n, alpha, beta)\n",
    "\n",
    "plt.figure(figsize = (8, 8))\n",
    "plt.scatter(data['f0'][(data['Y']==0)].values,data['f1'][(data['Y']==0)].values,color='r')\n",
    "plt.scatter(data['f0'][(data['Y']==1)].values,data['f1'][(data['Y']==1)].values,color='b')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Generally when we have features X and a target variable Y, our goal is to understand understand how Y varies with X.\n",
    "\n",
    "We can start by just plotting Y as a function of X. Since Y is binary we bin the X features and measure $E[Y|X_{bin}]$.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UkiRJUo9FsiRJktRjkSxJkiT1WCRLkiRJPRbJkiRJUo9FsiRJktRj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\nKioqKioqKiqlGCRHRUVFRUVFRUVFpfR/vrqGWvWMXDgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1200x700 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''\n",
    "We have 2 features and a target variable Y. Before we do any modeling, we can group the features\n",
    "and explore the relationship with Y visually\n",
    "'''\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "plt.figure(figsize=(12, 7))\n",
    "#Explore the effect of f0 and f1 by grouping and doing various tests\n",
    "cuts = np.arange(-10, 20, 2)/10.0\n",
    "data['f0_grp'] = pd.cut(data.f0.values, cuts)\n",
    "data['f1_grp'] = pd.cut(data.f1.values, cuts)\n",
    "d0 = data.groupby('f0_grp').mean()\n",
    "d1 = data.groupby('f1_grp').mean()\n",
    "\n",
    "#Now plot it\n",
    "k = len(d0['Y'])\n",
    "k_rng = np.arange(k)\n",
    "p = data['Y'].mean()\n",
    "\n",
    "xrng = np.arange(len(d0['Y']))\n",
    "\n",
    "ax1 = plt.subplot(211)\n",
    "plt.title('How Y varies with f0 and f1')\n",
    "ax1.bar(xrng, d0['Y'])\n",
    "ax1.plot(k_rng, p*np.ones(k), 'r-')\n",
    "ax1.set_xticks(0.4 + xrng)\n",
    "ax1.set_xticklabels(d1.index.values, rotation=20, size=8)\n",
    "\n",
    "\n",
    "ax2 = plt.subplot(212)\n",
    "ax2.bar(k_rng, d1['Y'])\n",
    "ax2.set_xticks(0.4 + xrng)\n",
    "ax2.set_xticklabels(d1.index.values, rotation=20, size=8)\n",
    "ax2.plot(k_rng, p*np.ones(k), 'r-')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to test the relationship between the features and the target is to use a logistic regression. In short, we want to fit a line $\\alpha+\\beta X$ such that:\n",
    "\n",
    "$P(Y|X)=f(X)$ where $f(X)=(1+e^{-(\\alpha+\\beta X)})^{-1}$\n",
    "\n",
    "In the next section we fit the model and then we plot it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NihUASJwbB8ATBCsAkDg3DoAnCFYAIHFuHABPEKwAQHLOh4vHx1/j3DgAGSJYAYDEuXEA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\nRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "logreg = linear_model.LogisticRegression(C=1e30)\n",
    "logreg.fit(data[['f0','f1']],data['Y'])\n",
    "\n",
    "def plot_dec_line(mn, mx, b0, b1, a, col, lab):\n",
    "    '''\n",
    "    This function plots the results of a bivariate logistic regression as a separating hyper-plane\n",
    "    '''\n",
    "    x = np.linspace(mn, mx, 100)\n",
    "    dec_line = list(map(lambda x_i: -1*(x_i*b0/b1 + a/b1), x))\n",
    "    plt.plot(x, dec_line, col, label = lab)\n",
    "    \n",
    "\n",
    "    \n",
    "#Now we'll plot the data, the fitted curve and the actual line\n",
    "plt.figure(figsize = (10, 10))\n",
    "plot_dec_line(0, 1, logreg.coef_[0][0], logreg.coef_[0][1], logreg.intercept_[0], 'black', 'Fitted')\n",
    "plot_dec_line(0, 1, beta[0], beta[1], alpha, 'green', 'Truth') \n",
    "plt.scatter(data['f0'][(data['Y']==0)].values, data['f1'][(data['Y']==0)].values, color='r')\n",
    "plt.scatter(data['f0'][(data['Y']==1)].values, data['f1'][(data['Y']==1)].values, color='b')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The nice thing about simulations is we know the truth and we can compare our learned model to the truth.  This is incredibly useful \n",
    "\n",
    "way to study the phenomenon of overfitting. In the above example we can compare the truth (that we created of course) to best answer\n",
    "\n",
    "given by the data.  Sometimes the fitted vs. truth lines don't match exactly. In extreme cases they are no where near each other.\n",
    "\n",
    "Let's see how the number of records affects this phenomenon.\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mysrK9PLLLyshIUHXX3+9iouLddFFF0W6azGn7mjdib0C/QM+m+o2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\niASICiwREREREZEA+f8BmCda6dSaCPgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1200x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_a_fit(alpha, beta, n):\n",
    "    '''\n",
    "    Generate a dataset and return a fitted model to it\n",
    "    '''    \n",
    "    dat_n = gen_logistic_dataframe(n, alpha, beta)\n",
    "    lr = linear_model.LogisticRegression(C=1e30)\n",
    "    return lr.fit(dat_n[['f0','f1']], dat_n['Y'])\n",
    "\n",
    "#Now get a few models with different sample sizes\n",
    "ms = [ get_a_fit(alpha, beta, 10**k) for k in range(1,7) ]\n",
    "\n",
    "#Now let's plot these against each other \n",
    "fig = plt.figure(figsize = (12, 6))\n",
    "for k in range(6):\n",
    "    ax = fig.add_subplot(2,3,k+1)\n",
    "    plt.title(\"n={}\".format(10**(k+1)))\n",
    "    plot_dec_line(0, 1, ms[k].coef_[0][0], ms[k].coef_[0][1], ms[k].intercept_[0], 'black', 'na')\n",
    "    plot_dec_line(0, 1, beta[0], beta[1], alpha, 'g', 'na')\n",
    "    ax.set_xlim(0, 1)\n",
    "    ax.set_ylim(0, 1)\n",
    "\n",
    "fig.tight_layout()\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Look at how much the black (fitted) line varies from the green (truth) line as we vary the size of the sample. With n=10, the fitted separating plane is nearly perpendicular to the truth. We only visibly fit the truth exactly when n=1 MM (though we come very close with a few orders of magnitude lower).  The lesson here is that with more data our fitted curve is expected to look more like the actual truth. Each realization of the green curve is a single estimate from one subset of some theoretically infinite data set. The fitted curve is essentially a function of the data. If we expect randomness across datasets (an artifact of sampling), we also should expect randomness in the curves we fit. The plot below illustrates this.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+yxZ/FUIipXP8BeYKJrVE6G+iJCuGWf2AhAAEqQ36zpWVuZ43Hk70EXRFFeI0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J2VtOp169b5p5/duP5LLgHuvLPmI5CB7hT0aeF1hBDSLL554nY5zDUSutZttLJffXP9rvCXZnEg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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (8, 8))\n",
    "\n",
    "ax = fig.add_subplot(111)\n",
    "for k in range(50):\n",
    "    try:\n",
    "        '''\n",
    "        I found that with small datasets of size=10, sometimes you generate a dataset with only 1 class.\n",
    "        This helps us get around that problem when it happens.\n",
    "        '''\n",
    "        mod = get_a_fit(alpha, beta, 100)     \n",
    "        plot_dec_line(0, 1, mod.coef_[0][0], mod.coef_[0][1], mod.intercept_[0], 'r.', 't')\n",
    "    except:\n",
    "        continue\n",
    "        \n",
    "plot_dec_line(0, 1, beta[0], beta[1], alpha, 'k', 't')\n",
    "ax.set_xlim(0, 1)\n",
    "ax.set_ylim(-1, 1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The black line here shows the truth. Each red line is a line fitted against a single realization of the data. Most are close to the\n",
    "\n",
    "truth, and it looks like E[red line]=black line. In real world situtations though we only get one data set. When your data is small\n",
    "\n",
    "(and model too complex), you might get unlucky and it up with a line that is very different from the theoretical truth. The red lines\n",
    "\n",
    "that are far off from the black lines are examples of unlucky overfitting. In real applications we'll likely never know the true \n",
    "\n",
    "underlying data distribution, but with the techniques taught in this course, we can at least be confident that overfitting can be \n",
    "\n",
    "avoided.</p>\n"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
